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- W2048941388 abstract "We develop an approach to multivariable cubature based on positivity, extension, and completion properties of moment matrices. We obtain a matrix-based lower bound on the size of a cubature rule of degree 2n + 1; for a planar measure μ, the bound is based on estimating ( rho (C): = inf { {text{rank}}(T - C):T{text{ Toeplitz and }}T geq C} , ) where C:=C# [μ ] is a positive matrix naturally associated with the moments of μ. We use this estimate to construct various minimal or near-minimal cubature rules for planar measures. In the case when C = diag(c1,...,cn) (including the case when μ is planar measure on the unit disk), ρ(C) is at least as large as the number of gaps ck >ck+1." @default.
- W2048941388 created "2016-06-24" @default.
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- W2048941388 date "2005-05-01" @default.
- W2048941388 modified "2023-10-13" @default.
- W2048941388 title "A Moment Matrix Approach to Multivariable Cubature" @default.
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- W2048941388 doi "https://doi.org/10.1007/s00020-003-1334-9" @default.
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